• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.859-863
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• 2003

We report on the theoretical positron affinities of closed-shell atomic anions. The second-order many-body perturbation theory is applied taking the positron-electron interaction as a perturbation. The corrections for the complete basis set effects to the second order affinity are calculated based on the variational and nonvariational energy functionals of explicitly correlated geminals. It is shown that the explicitly correlated methods accelerate the convergence of the expansion significantly giving the account of the cusp behavior outside the orbital space.

• Management Science and Financial Engineering
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• v.21 no.2
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• pp.25-30
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• 2015

This short article compares different solution methods for a basic RBC model (Hansen, 1985). We solve and simulate the model using two main algorithms: the methods of perturbation and projection, respectively. One novelty is that we offer a type of the hybrid method: we compute easily a second-order approximation to decision rules and use that approximation as an initial guess for finding Chebyshev polynomials. We also find that the second-order perturbation method is most competitive in terms of accuracy for standard RBC model.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.475-483
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• 2011

In this paper, we study the oscillatory and asymptotic behavior of a class of second order nonlinear differential inequality with perturbation and establish several theorems by using classification and analysis, which develop and generalize some known results.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• Journal of Korean Port Research
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• v.8 no.1
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• pp.41-47
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• 1994

The present paper discusses the nonlinear wave deformation due to a submerged coastal structure. Theory is based on the frequency-domain method using the third order perturbation and boundary integral method. Theoretical development to the second order perturbation and boundary integral method. Theoretical development to the second order Stokes wave for a bottom-seated submerged breakwater to the sea floor is newly expanded to the third order for a submerged coastal structure shown in Figure 1. Validity is demonstrated by comparing numerical results with the experimental ones of a rectangular air chamber structure, which has the same dimensions as that of this study. Nonlinear waves become larger and larger with wave propagation above the crown of the structure, and are transmitted to the onshore side of the structure. These characteristics are shown greatly as the increment of Ursell number on the structure. The total water profile depends largely on the phase lag among the first, second and third order component waves.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Computational Structural Engineering
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• v.9 no.4
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• pp.209-217
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• 1996

An Inverse modal perturbation method was applied to estimate the assessments of the damages at the large-scaled marine structure, such as pier or dolphin, from the structural dynamic natural frequencies and mode shape. Vibrations of structural stiffness, natural frequencies and mode shapes from the eigenvalue analysis lead to the modal peturbation equations, which were considered with a second order term. This paper estimates the assessments of the damages for the structure with the decreased stiffness and shows the convergence of perturbation equation.

• Journal of Korea Water Resources Association
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• v.34 no.6
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• pp.651-657
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• 2001

The second-order long waves generated by short wave groups propagating over a step are theoretically investigated. The diffraction of short waves is firstly formulated and the governing equations of second-order long waves are then derived by using a multiple-scale perturbation method. It is observed that free and locked long waves are generated and propagated with different velocities.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.373-392
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• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.75-82
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• 2020

In this study, the problem of torsion of bars with open cross section surrounded by corrugated boundaries is analyzed. An approximate analytical solution is given using perturbation technique. First, the stress analysis for circular open cross-section for arbitrary opening angle is formulated and the problem is analytically solved. Second, the open cross-section with corrugated cross section is analyzed using perturbation method. First order contributions to the stresses and the torques have been added. The results have been exemplified and compared by considering special examples.